The objective of the p-median problem is to identify p source locations and map them to n destinations while minimizing the average distance between destinations and corresponding sources. Several heuristic algorithms have been developed to solve this general class of facility location problems. In this study, we add to the current literature in two ways: (1) we present a thorough evaluation of existing classic heuristics and (2) we investigate the effect of spatial distribution of destination locations, and the number of sources and destinations on the performance of these algorithms for varying problem sizes using synthetic and real datasets. The performance of these algorithms is evaluated using the objective function value, time taken to achieve the solution, and the stability of the solution. The sensitivity of existing algorithms to the spatial distribution of destinations and scale of the problem with respect to the three metrics is analyzed in the paper. The utility of the study is demonstrated by evaluating these algorithms to select the locations of ad-hoc clinics that need to be set up for resource distribution during a bio-emergency. We demonstrate that interchange algorithms achieve good quality solutions with respect to both the execution time and cost function values, and they are more stable for clustered distributions.

p 中值问题的目标是识别 p 个源位置并将它们映射到 n 个目的地，同时最小化目的地和相应源之间的平均距离。已经开发了几种启发式算法来解决这类一般设施定位问题。在这项研究中，我们以两种方式对当前文献进行了补充：（1）我们对现有的经典启发式方法进行了全面评估；（2）我们研究了目的地位置的空间分布以及来源和目的地的数量对这些算法使用合成和真实数据集对不同问题大小的性能。这些算法的性能是使用目标函数值、实现解决方案所需的时间和解决方案的稳定性来评估的。本文分析了现有算法对目的地空间分布和问题规模的敏感性，并针对这三个指标进行了分析。该研究的实用性通过评估这些算法来选择需要在生物紧急情况下进行资源分配的临时诊所的位置来证明。我们证明了交换算法在执行时间和成本函数值方面都获得了高质量的解决方案，并且它们对于集群分布更稳定。